Domain Colouring

The color wheel method is a method to graphically represent complex functions. Complex functions represent the two-dimensional complex plane in turn, the real and imaginary values. The color circle method used amount r = |f(z)| and angle φ the complex function value f(z) around the display color of the function value set. According to r and φ the function value is selected the color from the color wheel. The amount defines the saturation and modulo is mapped to intervals . The first interval is 0 .. 1 then follow the intervals ( 1 .. e] , (e. .. e 2 ] , (e 2 ... e 3 ], etc. the color is defined by the angle and in 6 color zones starting with split blue from 0° to 60° and ending with green from 300° to 360°. the method is designed to that the function values ​​are close together are also displayed similar color. mapping the sums on intervals of the power of e corresponds to a logarithmic representation.

Colour Wheel

A compilation of a color wheel can be put together from different points depending on which state of affairs is to be visualized. The basis for the color circle the perception of similar colors. Leaving subjects with normal color pattern according to the sensation on similarity sort, which hues are usually brought in the same order. Beginning and end of the series are around so similar that the series can be closed to form a circle.

Complex function plot

The first two plots show the two complex functions with the color wheel method. The third plot shows the result function corresponding to the selected operation (+, -, * or /). The complex functions are given in the following form:

fz=Refxy+iImfxy

withz∈Candx, y∈Randz=x+iy

In the definition of the functions can be used the parameter a1[0]...a1[9] and b1[0]...b1[9]. The parameter can be adjusted by the slider. The parameter range is annotated at the slider in the form (start value:step:end value).